As an example he looks at rice. He writes
Although rice is the major foodstuff for about half of the world, it is highly protected and regulated. Only about 5 to 7 percent of the world’s rice production is traded across borders; that’s unusually low for an agricultural commodity.Cowen goes on to say
So when the price goes up — indeed, many varieties of rice have roughly doubled in price since 2007 — this highly segmented market means that the trade in rice doesn’t flow to the places of highest demand.
The more telling figure is that over the next year, international trade in rice is expected to decline more than 3 percent, when it should be expanding. The decline is attributable mainly to recent restrictions on rice exports in rice-producing countries like India, Indonesia, Vietnam, China, Cambodia and Egypt.The problem here is, of course, the incentives export restrictions give. When export restrictions are placed on any good it sends a message to producers of that good that their output is least profitable precisely when it is needed most. Restricted exports increases the local supply which reduces the local price, which reduces the return for local producers. In the case of rice this means that there is little incentive to plant, harvest or store rice. High prices should give producers the incentive to expand production, which is just what is needed for rice. But if producers can not access those high prices on the world market because of export restrictions, then they don't have the incentive needed. Cowen notes
Restrictions on the rice trade run the risk of making shortages and high prices permanent. Export restrictions treat rice trade and production as a zero- or negative-sum game where one country’s gain comes at the expense of another.There are few areas in which free trade could do more good, than in the production of food.
Update: Not PC makes the point that When producing becomes illegal, prices go through the roof.